5,641 research outputs found
Mellin-Barnes integrals as Fourier-Mukai transforms
We study the generalized hypergeometric system introduced by Gelfand,
Kapranov and Zelevinsky and its relationship with the toric Deligne-Mumford
(DM) stacks recently studied by Borisov, Chen and Smith. We construct series
solutions with values in a combinatorial version of the Chen-Ruan (orbifold)
cohomology and in the -theory of the associated DM stacks. In the spirit of
the homological mirror symmetry conjecture of Kontsevich, we show that the
-theory action of the Fourier-Mukai functors associated to basic toric
birational maps of DM stacks are mirrored by analytic continuation
transformations of Mellin-Barnes type.Comment: 55 pages, LaTe
Homogenization of the planar waveguide with frequently alternating boundary conditions
We consider Laplacian in a planar strip with Dirichlet boundary condition on
the upper boundary and with frequent alternation boundary condition on the
lower boundary. The alternation is introduced by the periodic partition of the
boundary into small segments on which Dirichlet and Neumann conditions are
imposed in turns. We show that under the certain condition the homogenized
operator is the Dirichlet Laplacian and prove the uniform resolvent
convergence. The spectrum of the perturbed operator consists of its essential
part only and has a band structure. We construct the leading terms of the
asymptotic expansions for the first band functions. We also construct the
complete asymptotic expansion for the bottom of the spectrum
Propagation of axions in a strongly magnetized medium
The polarization operator of an axion in a degenerate gas of electrons
occupying the ground-state Landau level in a superstrong magnetic field G is investigated in a model with a
tree-level axion-electron coupling. It is shown that a dynamic axion mass,
which can fall within the allowed range of values , is generated under the conditions of strongly
magnetized neutron stars. As a result, the dispersion relation for axions is
appreciably different from that in a vacuum.Comment: RevTex, no figures, 13 pages, Revised version of the paper published
in J. Exp. Theor. Phys. {\bf 88}, 1 (1999
Asymptotic behaviour of the spectrum of a waveguide with distant perturbations
We consider the waveguide modelled by a -dimensional infinite tube. The
operator we study is the Dirichlet Laplacian perturbed by two distant
perturbations. The perturbations are described by arbitrary abstract operators
''localized'' in a certain sense, and the distance between their ''supports''
tends to infinity. We study the asymptotic behaviour of the discrete spectrum
of such system. The main results are a convergence theorem and the asymptotics
expansions for the eigenvalues. The asymptotic behaviour of the associated
eigenfunctions is described as well. We also provide some particular examples
of the distant perturbations. The examples are the potential, second order
differential operator, magnetic Schroedinger operator, curved and deformed
waveguide, delta interaction, and integral operator
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